Question 02- We will derive the moment of inertia of a hollow cylinder of inner radius, Router radius, R. and height, h

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Question 02 We Will Derive The Moment Of Inertia Of A Hollow Cylinder Of Inner Radius Router Radius R And Height H 1 (51.03 KiB) Viewed 32 times

Question 02- We will derive the moment of inertia of a hollow cylinder of inner radius, Router radius, R. and height, h (a) First, sketch the incremental mass, dm, having incremental volume, dv, that you will use to "build out the in steps. We will assume that the cylinder is made of material with uniform volumetric density.p hollow cylinder. Be certain to label all features including any dimensional lengths for full credit. (5 points) z-axis: along the central axis of hollow cylinder Part (a)- Sketch the incremental mass, dm, with incremental volume, dv, labelling all dimensions. Router Rinner x=p2ordrh 3 (b) Use the definitional relationship that/= f r²dm to set up the integral that you will use to find the resulting moment of inertia of the hollow cylinder rotated about its central axis as shown above. (5 points) (c) Evaluate the integral that you have set up above in order to derive an equation for the moment of inertia in terms of p, h, Rincer, and Router (5 points)... (d) Solve for the total mass, M, of the hollow cylinder by integration of dm in terms of p, h, Reer, and Router (5 points) (e) Combine your above results from part (c) and part (d) to provide the moment of inertia of a uniform density material, hollow cylinder (pictured in above figure) rotated about its central axis in terms of M, Recer, and Router Potentially Useful Hint: Recall that the wonderful CCC Math Professor Carol Stanton once told you that (a - b) = (a² − b ² ) (a² + b²) (5 points) r?